# Libraries to help with reading and manipulating data
import pandas as pd
import numpy as np

# Libraries to help with data visualization
import matplotlib.pyplot as plt
import seaborn as sns

sns.set_theme(style='darkgrid')

# Removes the limit for the number of displayed columns
pd.set_option("display.max_columns", None)
# Sets the limit for the number of displayed rows
pd.set_option("display.max_rows", 200)

# Scale the data using z-score
from sklearn.preprocessing import StandardScaler

# Z-score for outlier detection
from scipy.stats import zscore

# Compute distances
from scipy.spatial.distance import cdist

# Perform k-means clustering and compute silhouette scores
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score

# Perform PCA and GMM
from sklearn.decomposition import PCA
from sklearn.mixture import GaussianMixture

# Visualize the elbow curve and silhouette scores
from yellowbrick.cluster import KElbowVisualizer, SilhouetteVisualizer

# Suppress warnings
import warnings
warnings.filterwarnings("ignore")

from google.colab import drive
drive.mount('/content/drive')

Mounted at /content/drive

# Load marketing dataset into a pandas dataframe, check file presence and provide useful output
import os

file_path = "/content/drive/MyDrive/marketing_campaign.csv"
if os.path.exists(file_path):
    data = pd.read_csv(file_path, sep="\t")
    print("Dataset loaded.")
else:
    print("File not found:", file_path)

Dataset loaded.

data.shape

(2240, 29)

# Checking datatypes and number of non-null values for each column
data.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 2240 entries, 0 to 2239
Data columns (total 29 columns):
 #   Column               Non-Null Count  Dtype  
---  ------               --------------  -----  
 0   ID                   2240 non-null   int64  
 1   Year_Birth           2240 non-null   int64  
 2   Education            2240 non-null   object 
 3   Marital_Status       2240 non-null   object 
 4   Income               2216 non-null   float64
 5   Kidhome              2240 non-null   int64  
 6   Teenhome             2240 non-null   int64  
 7   Dt_Customer          2240 non-null   object 
 8   Recency              2240 non-null   int64  
 9   MntWines             2240 non-null   int64  
 10  MntFruits            2240 non-null   int64  
 11  MntMeatProducts      2240 non-null   int64  
 12  MntFishProducts      2240 non-null   int64  
 13  MntSweetProducts     2240 non-null   int64  
 14  MntGoldProds         2240 non-null   int64  
 15  NumDealsPurchases    2240 non-null   int64  
 16  NumWebPurchases      2240 non-null   int64  
 17  NumCatalogPurchases  2240 non-null   int64  
 18  NumStorePurchases    2240 non-null   int64  
 19  NumWebVisitsMonth    2240 non-null   int64  
 20  AcceptedCmp3         2240 non-null   int64  
 21  AcceptedCmp4         2240 non-null   int64  
 22  AcceptedCmp5         2240 non-null   int64  
 23  AcceptedCmp1         2240 non-null   int64  
 24  AcceptedCmp2         2240 non-null   int64  
 25  Complain             2240 non-null   int64  
 26  Z_CostContact        2240 non-null   int64  
 27  Z_Revenue            2240 non-null   int64  
 28  Response             2240 non-null   int64  
dtypes: float64(1), int64(25), object(3)
memory usage: 507.6+ KB

pd.concat([data.head(), data.iloc[-10:]])

# Create a new 'Age' feature to replace 'Year_Birth' (which is less usable for segmentation purposes)
from datetime import date
current_year = date.today().year
data['Age'] = current_year - data['Year_Birth']

# Calculate the average age
print("Mean Age is:", data['Age'].mean())

# Calculate the median age
print("Median Age is:", data['Age'].median())

Mean Age is: 56.19419642857143
Median Age is: 55.0

# Copying the data to another variable to avoid any changes to original data
data = data.copy()

# Check the statistical summary of the data
data.describe(include = 'all').T

# Check for missing values
data.isnull().sum()

from sklearn.impute import SimpleImputer

# Create a SimpleImputer to fill missing 'Income' values with the median
# Using median is usually preferred for income since it is less sensitive to outliers
income_imputer = SimpleImputer(strategy='median')

# Fit and transform the imputer only on the 'Income' column
data['Income'] = income_imputer.fit_transform(data[['Income']])

# Check for duplicate values
data.duplicated().sum()

np.int64(0)

# Drop columns containing unique IDs, repetitive campaign information,
# and other metadata that are not informative for clustering analysis
columns_to_drop = [col for col in [
    'Dt_Customer', 'Year_Birth', 'ID',
    'AcceptedCmp1', 'AcceptedCmp2', 'AcceptedCmp3',
    'AcceptedCmp4', 'AcceptedCmp5', 'Education',
    'Marital_Status', 'Z_CostContact', 'Z_Revenue',] if col in data.columns]
data.drop(columns=columns_to_drop, inplace=True)

data.shape

(2240, 18)

# Defining the figure size
plt.figure(figsize=(12, 10))

# Iterating through each column
# Assigning a subplot in the main plot
# Plotting the histogram
for i, feature in enumerate(data.select_dtypes(include='number').columns):
    plt.subplot(6, 3, i+1)
    sns.histplot(data=data, x=feature, kde = True)

# Add spacing between plots
plt.tight_layout();

# Defining the figure size
plt.figure(figsize=(12, 10))

# Plotting the boxplot for each numerical feature
# Iterating through each column (see: previous cell)
for i, feature in enumerate(data.select_dtypes(include='number').columns):
    plt.subplot(6, 3, i+1)
    sns.boxplot(data=data, x=feature)

plt.tight_layout();

# Check for correlations
plt.figure(figsize=(15, 7))
sns.heatmap(data.corr(), annot=True, cmap='coolwarm')
plt.show()

# Check for pairplots
sns.pairplot(data=data, diag_kind="kde")
plt.show()

# Selection of original numeric variables
numeric_data = data.select_dtypes(include='number')

# Z-score calculation and outliers detection
z_scores = np.abs(zscore(numeric_data))
outliers = (z_scores > 3).any(axis=1)

print(f"Number of detected outliers using Z-score method: {outliers.sum()}")

Number of detected outliers using Z-score method: 282

# Creating a copy of the original data
k_means_data = data.copy()

# Standardizing the numerical features and scaling the data before clustering
scaler = StandardScaler()
scaled_data = scaler.fit_transform(k_means_data)

# Creating a dataframe of the scaled data
scaled_df = pd.DataFrame(scaled_data, columns=k_means_data.columns)

clusters = range(2, 11)
wcss_k8 = []

# Initializing the kmeans model
for k in clusters:
    model = KMeans(n_clusters=k, random_state=0)
    # Fitting the kmeans model on the scaled data
    model.fit(scaled_df)
    wcss = model.inertia_
    wcss_k8.append(wcss)

    print("Number of Clusters:", k, "\tWCSS:", wcss)

plt.plot(clusters, wcss_k8, "bx-", marker='o')
plt.xlabel("k")
plt.ylabel("WCSS")
plt.title("Selecting k with the Elbow Method", fontsize=20)
plt.show()

Number of Clusters: 2 	WCSS: 29497.59180741321
Number of Clusters: 3 	WCSS: 26230.807971388716
Number of Clusters: 4 	WCSS: 24835.86779461125
Number of Clusters: 5 	WCSS: 22712.065378166288
Number of Clusters: 6 	WCSS: 21683.006732992202
Number of Clusters: 7 	WCSS: 20721.29101573217
Number of Clusters: 8 	WCSS: 19867.13268970371
Number of Clusters: 9 	WCSS: 19394.819190201433
Number of Clusters: 10 	WCSS: 18860.74162517017

sil_score = []
cluster_list = range(2, 11)

# Initializing the kmeans model
for n_clusters in cluster_list:
    clusterer = KMeans(n_clusters=n_clusters, random_state=0)
    # Fitting the kmeans model
    preds = clusterer.fit_predict(scaled_df)
    # Checking the silhouette score against the predictions
    score = silhouette_score(scaled_df, preds)
    sil_score.append(score)
    print("For n_clusters = {}, the silhouette score is {}".format(n_clusters, score))

For n_clusters = 2, the silhouette score is 0.28417340291067655
For n_clusters = 3, the silhouette score is 0.21157332525513017
For n_clusters = 4, the silhouette score is 0.14392835398979065
For n_clusters = 5, the silhouette score is 0.1507865356301614
For n_clusters = 6, the silhouette score is 0.14593106430611189
For n_clusters = 7, the silhouette score is 0.1483993804513877
For n_clusters = 8, the silhouette score is 0.15445670830945524
For n_clusters = 9, the silhouette score is 0.15201513952801726
For n_clusters = 10, the silhouette score is 0.16112726430616614

plt.plot(cluster_list, sil_score, marker = 'o')
plt.show()

# Create the model with k=4
model = KMeans(n_clusters=4, random_state=0)

# Fit the silhouette visualizer
visualizer = SilhouetteVisualizer(model)

visualizer.fit(scaled_df)
visualizer.show()

<Axes: title={'center': 'Silhouette Plot of KMeans Clustering for 2240 Samples in 4 Centers'}, xlabel='silhouette coefficient values', ylabel='cluster label'>

%%time

# Initializing kmeans model
kmeans = KMeans(n_clusters=4, random_state=0)
cluster_labels = kmeans.fit_predict(scaled_df)

CPU times: user 9.67 ms, sys: 0 ns, total: 9.67 ms
Wall time: 9.26 ms

# Perform PCA to reduce the data to 2 principal components
pca = PCA(n_components=2)
reduced = pca.fit_transform(scaled_df)

# Create a scatter plot
plt.figure(figsize=(8,6))
plt.scatter(reduced[:,0], reduced[:,1], c=cluster_labels, cmap='viridis')
plt.title("PCA Projection with KMeans Clusters")
plt.show()

# Fit GMM (assuming 4 clusters for consistency with kmeans)
gmm = GaussianMixture(n_components=4, random_state=0)
gmm_labels = gmm.fit_predict(scaled_df)

# PCA projection
plt.figure(figsize=(8, 6))
sns.scatterplot(
    x=reduced[:, 0],
    y=reduced[:, 1],
    hue=gmm_labels,
    palette="tab10",
    legend="full",
    s=30
)
plt.title("PCA Projection with GMM Clusters")
plt.xlabel("PCA 1")
plt.ylabel("PCA 2")
plt.legend(title="Cluster")
plt.grid(True)
plt.tight_layout()
plt.show()

# Fit kmeans model with k=4 and get cluster labels
kmeans = KMeans(n_clusters=4, random_state=0)
kmeans_labels = kmeans.fit_predict(scaled_df)

# Fit GMM with k=4 and get cluster labels
gmm = GaussianMixture(n_components=4, random_state=0)
gmm_labels = gmm.fit_predict(scaled_df)

# Compute silhouette scores for both
kmeans_score = silhouette_score(scaled_df, kmeans_labels)
gmm_score = silhouette_score(scaled_df, gmm_labels)

# Print silhouette score comparison
print("Silhouette Score Comparison")
print(f"K-Means Silhouette Score: {kmeans_score:.4f}")
print(f"GMM Silhouette Score:     {gmm_score:.4f}")

Silhouette Score Comparison
K-Means Silhouette Score: 0.1439
GMM Silhouette Score:     0.1244

# Creating a copy of the original data
clusterdataset = data.copy()

# Adding cluster labels to the scaled dataframes
clusterdataset["K_means_segments"] = cluster_labels

# Customer count per cluster
clusterdataset["K_means_segments"].value_counts().sort_index()

# Visualizing the number of customers in each kmeans cluster
plt.figure(figsize=(8, 6))
sns.countplot(data=clusterdataset, x="K_means_segments", palette="pastel")

plt.title("Number of Customers per Cluster", fontsize=16)
plt.xlabel("Cluster")
plt.ylabel("Count")
plt.xticks(rotation=0)
plt.grid(axis="y", linestyle="--", alpha=0.7)

plt.tight_layout()
plt.show()

# Set the figure size for the plot and the main title
plt.figure(figsize=(24, 24))
plt.suptitle("Boxplot of numerical variables for each cluster in KMeans Clustering", fontsize=20)

# Iterate over each numerical variable in the dataframe
for i, variable in enumerate(clusterdataset.columns.to_list()[:-1]):
    # Create subplots in a 6x3 grid
    plt.subplot(6, 3, i + 1)
    sns.boxplot(data=clusterdataset, x="K_means_segments", y=variable, palette='Spectral')

# Adjust layout to make space for title
plt.tight_layout(rect=[0, 0, 1, 0.96])
plt.show()

# Plotting barplots of numerical variables for each cluster
# Set the figure size for the plot and the main title
plt.figure(figsize=(20, 20))
plt.suptitle("Barplots of all variables for each cluster", fontsize=20)

for i, variable in enumerate(clusterdataset.columns.to_list()[:-1]):
    plt.subplot(6, 3, i + 1)
    sns.barplot(data=clusterdataset, x="K_means_segments", y=variable, palette='Spectral')
    plt.title(variable)

plt.tight_layout(pad=2.0)
plt.show()

# Compute the mean of all numerical features grouped by kmeans cluster
cluster_summary = clusterdataset.groupby("K_means_segments").mean(numeric_only=True)

# Display the summary table for cluster profiling
display(cluster_summary)

# Create barplots for each numerical variable in order to compare cluster means
plt.figure(figsize=(20, 20))
plt.suptitle("Barplots of Feature Means per Cluster", fontsize=20)

for i, column in enumerate(cluster_summary.columns):
    plt.subplot(6, 3, i + 1)
    sns.barplot(x=cluster_summary.index, y=cluster_summary[column], palette="Spectral")
    plt.title(column)
    plt.xlabel("Cluster")
    plt.ylabel("Mean Value")

plt.tight_layout(pad=2.0)
plt.show()

	count	unique	top	freq	mean	std	min	25%	50%	75%	max
ID	2240.0	NaN	NaN	NaN	5592.159821	3246.662198	0.0	2828.25	5458.5	8427.75	11191.0
Year_Birth	2240.0	NaN	NaN	NaN	1968.805804	11.984069	1893.0	1959.0	1970.0	1977.0	1996.0
Education	2240	5	Graduation	1127	NaN	NaN	NaN	NaN	NaN	NaN	NaN
Marital_Status	2240	8	Married	864	NaN	NaN	NaN	NaN	NaN	NaN	NaN
Income	2216.0	NaN	NaN	NaN	52247.251354	25173.076661	1730.0	35303.0	51381.5	68522.0	666666.0
Kidhome	2240.0	NaN	NaN	NaN	0.444196	0.538398	0.0	0.0	0.0	1.0	2.0
Teenhome	2240.0	NaN	NaN	NaN	0.50625	0.544538	0.0	0.0	0.0	1.0	2.0
Dt_Customer	2240	663	31-08-2012	12	NaN	NaN	NaN	NaN	NaN	NaN	NaN
Recency	2240.0	NaN	NaN	NaN	49.109375	28.962453	0.0	24.0	49.0	74.0	99.0
MntWines	2240.0	NaN	NaN	NaN	303.935714	336.597393	0.0	23.75	173.5	504.25	1493.0
MntFruits	2240.0	NaN	NaN	NaN	26.302232	39.773434	0.0	1.0	8.0	33.0	199.0
MntMeatProducts	2240.0	NaN	NaN	NaN	166.95	225.715373	0.0	16.0	67.0	232.0	1725.0
MntFishProducts	2240.0	NaN	NaN	NaN	37.525446	54.628979	0.0	3.0	12.0	50.0	259.0
MntSweetProducts	2240.0	NaN	NaN	NaN	27.062946	41.280498	0.0	1.0	8.0	33.0	263.0
MntGoldProds	2240.0	NaN	NaN	NaN	44.021875	52.167439	0.0	9.0	24.0	56.0	362.0
NumDealsPurchases	2240.0	NaN	NaN	NaN	2.325	1.932238	0.0	1.0	2.0	3.0	15.0
NumWebPurchases	2240.0	NaN	NaN	NaN	4.084821	2.778714	0.0	2.0	4.0	6.0	27.0
NumCatalogPurchases	2240.0	NaN	NaN	NaN	2.662054	2.923101	0.0	0.0	2.0	4.0	28.0
NumStorePurchases	2240.0	NaN	NaN	NaN	5.790179	3.250958	0.0	3.0	5.0	8.0	13.0
NumWebVisitsMonth	2240.0	NaN	NaN	NaN	5.316518	2.426645	0.0	3.0	6.0	7.0	20.0
AcceptedCmp3	2240.0	NaN	NaN	NaN	0.072768	0.259813	0.0	0.0	0.0	0.0	1.0
AcceptedCmp4	2240.0	NaN	NaN	NaN	0.074554	0.262728	0.0	0.0	0.0	0.0	1.0
AcceptedCmp5	2240.0	NaN	NaN	NaN	0.072768	0.259813	0.0	0.0	0.0	0.0	1.0
AcceptedCmp1	2240.0	NaN	NaN	NaN	0.064286	0.245316	0.0	0.0	0.0	0.0	1.0
AcceptedCmp2	2240.0	NaN	NaN	NaN	0.013393	0.114976	0.0	0.0	0.0	0.0	1.0
Complain	2240.0	NaN	NaN	NaN	0.009375	0.096391	0.0	0.0	0.0	0.0	1.0
Z_CostContact	2240.0	NaN	NaN	NaN	3.0	0.0	3.0	3.0	3.0	3.0	3.0
Z_Revenue	2240.0	NaN	NaN	NaN	11.0	0.0	11.0	11.0	11.0	11.0	11.0
Response	2240.0	NaN	NaN	NaN	0.149107	0.356274	0.0	0.0	0.0	0.0	1.0
Age	2240.0	NaN	NaN	NaN	56.194196	11.984069	29.0	48.0	55.0	66.0	132.0

	count
K_means_segments
0	550
1	575
2	547
3	568

	Income	Kidhome	Teenhome	Recency	MntWines	MntFruits	MntMeatProducts	MntFishProducts	MntSweetProducts	MntGoldProds	NumDealsPurchases	NumWebPurchases	NumCatalogPurchases	NumStorePurchases	NumWebVisitsMonth	Complain	Response	Age
K_means_segments
0	42436.047273	0.690909	0.961818	50.658182	68.550909	4.249091	25.441818	6.081818	4.341818	14.507273	2.445455	2.296364	0.710909	3.580000	5.894545	0.010909	0.052727	61.676364
1	76695.117391	0.041739	0.158261	49.646957	591.645217	69.584348	460.306087	101.177391	71.488696	77.813913	1.314783	5.166957	5.996522	8.321739	2.826087	0.005217	0.292174	56.493913
2	59643.780622	0.193784	0.936015	47.773309	516.972578	23.491773	145.023766	30.970750	24.292505	64.787934	3.678245	6.583181	3.329068	8.082267	5.654479	0.009141	0.118830	60.425960
3	29838.729754	0.853873	0.003521	48.352113	35.445423	6.547535	28.117958	9.848592	6.758803	18.394366	1.927817	2.315141	0.533451	3.160211	6.952465	0.012324	0.126761	46.507042

Problem Statement¶

Business Context¶

Objective¶

Data Dictionary¶

Let's start coding!¶

Importing necessary libraries¶

Loading the data¶

Data Overview¶

Question 1: What are the data types of all the columns?¶

Observations: The dataset has 2,240 entries and 29 columns. It contains 24 integer columns, 1 float column, and 4 object columns. The mean age is around 56 years.¶

Question 2: Check the statistical summary of the data. What is the average household income?¶

Observations: The average household income is 52247.25, as shown in the statistical summary.¶

Question 3: Are there any missing values in the data? If yes, treat them using an appropriate method¶

Observations: Yes, there are 24 missing values in the `Income` column. I treated them using median imputation, because the income distribution is skewed and the median is more robust to outliers.¶

Question 4: Are there any duplicates in the data?¶

Observations: There are no duplicates in the data. Therefore, there is no need to drop them using: data.drop_duplicates(inplace=True).¶

Exploratory Data Analysis¶

Univariate Analysis¶

Question 5: Explore all the variables and provide observations on their distributions. (histograms and boxplots)¶

Bivariate Analysis¶

Question 6: Perform multivariate analysis to explore the relationsips between the variables.¶

K-means Clustering¶

Question 7 : Select the appropriate number of clusters using the elbow Plot. What do you think is the appropriate number of clusters?¶

Observations: The optimal number of clusters appears to be 4, because this is the point at which the rate of decrease in WCSS begins to flatten. I believe that, beyond this value, adding more clusters shall provide minimal benefit.¶

Question 8 : finalize appropriate number of clusters by checking the silhoutte score as well. Is the answer different from the elbow plot?¶

Question 9: Do a final fit with the appropriate number of clusters. How much total time does it take for the model to fit the data?¶

Cluster Profiling and Comparison¶

Question 10: Perform cluster profiling using boxplots for the K-Means algorithm. Analyze key characteristics of each cluster and provide detailed observations.¶

Observations: The clusters have different patterns:¶

Question 11: Perform cluster profiling on the data using a barplot for the K-Means algorithm. Provide insights and key observations for each cluster based on the visual analysis.¶

Observations: The cluster profile using barplots shows some differences between the segments:¶

Business Recommedations¶

Question 12: Based on the cluster insights, what business recommendations can be provided?¶

	ID	Year_Birth	Education	Marital_Status	Income	Kidhome	Teenhome	Dt_Customer	Recency	MntWines	MntFruits	MntMeatProducts	MntFishProducts	MntSweetProducts	MntGoldProds	NumDealsPurchases	NumWebPurchases	NumCatalogPurchases	NumStorePurchases	NumWebVisitsMonth	AcceptedCmp3	AcceptedCmp4	AcceptedCmp1	Z_CostContact	Z_Revenue	Response
0	5524	1957	Graduation	Single	58138.0	0	0	04-09-2012	58	635	88	546	172	88	88	3	8	10	4	7	0	0	0	3	11	1
1	2174	1954	Graduation	Single	46344.0	1	1	08-03-2014	38	11	1	6	2	1	6	2	1	1	2	5	0	0	0	3	11	0
2	4141	1965	Graduation	Together	71613.0	0	0	21-08-2013	26	426	49	127	111	21	42	1	8	2	10	4	0	0	0	3	11	0
3	6182	1984	Graduation	Together	26646.0	1	0	10-02-2014	26	11	4	20	10	3	5	2	2	0	4	6	0	0	0	3	11	0
4	5324	1981	PhD	Married	58293.0	1	0	19-01-2014	94	173	43	118	46	27	15	5	5	3	6	5	0	0	0	3	11	0
2230	7004	1984	Graduation	Single	11012.0	1	0	16-03-2013	82	24	3	26	7	1	23	3	3	1	2	9	1	0	0	3	11	0
2231	9817	1970	Master	Single	44802.0	0	0	21-08-2012	71	853	10	143	13	10	20	2	9	4	12	8	0	0	0	3	11	0
2232	8080	1986	Graduation	Single	26816.0	0	0	17-08-2012	50	5	1	6	3	4	3	1	0	0	3	4	0	0	0	3	11	0
2233	9432	1977	Graduation	Together	666666.0	1	0	02-06-2013	23	9	14	18	8	1	12	4	3	1	3	6	0	0	0	3	11	0
2234	8372	1974	Graduation	Married	34421.0	1	0	01-07-2013	81	3	3	7	6	2	9	1	1	0	2	7	0	0	0	3	11	0
2235	10870	1967	Graduation	Married	61223.0	0	1	13-06-2013	46	709	43	182	42	118	247	2	9	3	4	5	0	0	0	3	11	0
2236	4001	1946	PhD	Together	64014.0	2	1	10-06-2014	56	406	0	30	0	0	8	7	8	2	5	7	0	0	1	3	11	0
2237	7270	1981	Graduation	Divorced	56981.0	0	0	25-01-2014	91	908	48	217	32	12	24	1	2	3	13	6	0	1	0	3	11	0
2238	8235	1956	Master	Together	69245.0	0	1	24-01-2014	8	428	30	214	80	30	61	2	6	5	10	3	0	0	0	3	11	0
2239	9405	1954	PhD	Married	52869.0	1	1	15-10-2012	40	84	3	61	2	1	21	3	3	1	4	7	0	0	0	3	11	1

Problem Statement¶

Business Context¶

Objective¶

Data Dictionary¶

Let's start coding!¶

Importing necessary libraries¶

Loading the data¶

Data Overview¶

Question 1: What are the data types of all the columns?¶

Observations: The dataset has 2,240 entries and 29 columns. It contains 24 integer columns, 1 float column, and 4 object columns. The mean age is around 56 years.¶

Question 2: Check the statistical summary of the data. What is the average household income?¶

Observations: The average household income is 52247.25, as shown in the statistical summary.¶

Question 3: Are there any missing values in the data? If yes, treat them using an appropriate method¶

Observations: Yes, there are 24 missing values in the Income column. I treated them using median imputation, because the income distribution is skewed and the median is more robust to outliers.¶

Question 4: Are there any duplicates in the data?¶

Observations: There are no duplicates in the data. Therefore, there is no need to drop them using: data.drop_duplicates(inplace=True).¶

Exploratory Data Analysis¶

Univariate Analysis¶

Question 5: Explore all the variables and provide observations on their distributions. (histograms and boxplots)¶

Bivariate Analysis¶

Question 6: Perform multivariate analysis to explore the relationsips between the variables.¶

K-means Clustering¶

Question 7 : Select the appropriate number of clusters using the elbow Plot. What do you think is the appropriate number of clusters?¶

Observations: The optimal number of clusters appears to be 4, because this is the point at which the rate of decrease in WCSS begins to flatten. I believe that, beyond this value, adding more clusters shall provide minimal benefit.¶

Question 8 : finalize appropriate number of clusters by checking the silhoutte score as well. Is the answer different from the elbow plot?¶

Question 9: Do a final fit with the appropriate number of clusters. How much total time does it take for the model to fit the data?¶

Cluster Profiling and Comparison¶

Question 10: Perform cluster profiling using boxplots for the K-Means algorithm. Analyze key characteristics of each cluster and provide detailed observations.¶

Observations: The clusters have different patterns:¶

Question 11: Perform cluster profiling on the data using a barplot for the K-Means algorithm. Provide insights and key observations for each cluster based on the visual analysis.¶

Observations: The cluster profile using barplots shows some differences between the segments:¶

Business Recommedations¶

Question 12: Based on the cluster insights, what business recommendations can be provided?¶

Observations: Yes, there are 24 missing values in the `Income` column. I treated them using median imputation, because the income distribution is skewed and the median is more robust to outliers.¶